The same example given in xy-pic done in Tikz:
More examples and code are at 
http://www.texample.net/tikz/examples/ 
and the manual http://mirror.ctan.org/graphics/pgf/base/doc/generic/pgf/pgfmanual.pdf

    \documentclass[a4paper]{article}
    \usepackage{tikz}
    \usetikzlibrary{shapes}
    \begin{document}
    \begin{tikzpicture}[shorten <=7pt,shorten >=7pt]
        \node [name=oct,regular polygon,regular polygon sides=4,minimum size= 12em] {};
        \node at (oct.corner 1) [name=octCorner1] {$Z$};
        \node at (oct.corner 2) [name=octCorner2] {$X'$};
        \node at (oct.corner 3) [name=octCorner3] {$Z'$};
        \node at (oct.corner 4) [name=octCorner4] {$X$};
        \node at (oct.center) [name=octCenter] {$Y$};
        \draw [-stealth] (oct.corner 2) -- node [right] {$[1]$} (oct.corner 3);
        \draw [-stealth] (oct.corner 1) --                      (oct.corner 2);
        \draw [-stealth] (oct.corner 1) --                      (oct.corner 4);
        \draw [-stealth] (oct.corner 3) -- node [above] {$[1]$} (oct.corner 4);
        \draw [-stealth] (oct.corner 2) -- node [right] {$[1]$} (oct.center);
        \draw [-stealth] (oct.corner 4) --                      (oct.center);
        \draw [-stealth] (oct.center)   --                      (oct.corner 3);
        \draw [-stealth] (oct.center)   --                      (oct.corner 1);
    \end{tikzpicture}
    \end{document}


----------
Changed from an octagon.